Existence of normalized solutions to Choquard equation with general mixed nonlinearities

We study the existence of normalized solutions to the following Choquard equation with F being a Berestycki-Lions type function {equation*} {cases} -Δ u+λ u=(Iα F(u))f(u), in\ R^N, \\ ∫R^N|u|^2dx=ρ^2, {cases} {equation*} where N≥ 3, ρ>0 is assigned, α∈ (0,N), Iα is the Riesz potential, and λ∈ R is an unknown parameter that appears as a Lagrange multiplier. Here, the general nonlinearity F contains the L²-subcritical and L²-supercritical mixed case, the Hardy-Littlewood-Sobolev lower critical and upper critical cases.